Answer:
\(r_{1} = 26\).
Step-by-step explanation:
Given : the ratio of the circumferences of two circles is 2:3. If the large circle has a radius of 39 cm,
To find : what is the radius of the small circle.
Solution : We have given that ratio of the circumferences of two circles is 2:3.
Let \(r_{2}\) is radius of larger circle and \(r_{1}\) is radius of small circle .
Then circumference = \(\frac{2\pi\ r_{1} }{2\pi\ r_{2}}\) = \(\frac{2}{3}\) .
Solving the above equation
\(\frac{r_{1}}{r_{2} }\) = \(\frac{2}{3}\) .
We have given radius of larger circle = 39 then
\(\frac{r_{1}}{39}\) = \(\frac{2}{3}\) .
On multiplying both sides by 39.
\(r_{1} = 39 *\frac{2}{3}\).
\(r_{1} = 13 * 2\).
\(r_{1} = 26\).
Therefore, \(r_{1} = 26\).
